def 	_UpperCamelCase (      snake_case__				)    -> int:
							__UpperCAmelCase    :      Optional[Any]       = len(_lowerCamelCase				)
							__UpperCAmelCase    :      Any       = len(matrix[0]				)
							__UpperCAmelCase    :      Optional[int]       = min(_lowerCamelCase,     _lowerCamelCase				)

							for row in range(_lowerCamelCase				):
														# Check if diagonal element is not zero
														if matrix[row][row] != 0:
																					# Eliminate all the elements below the diagonal
																					for col in range(row + 1,     _lowerCamelCase				):
																												__UpperCAmelCase    :      Dict       = matrix[col][row] / matrix[row][row]
																												for i in range(_lowerCamelCase,     _lowerCamelCase				):
																																			matrix[col][i] -= multiplier * matrix[row][i]
														else:
																					# Find a non-zero diagonal element to swap rows
																					__UpperCAmelCase    :      List[str]       = True
																					for i in range(row + 1,     _lowerCamelCase				):
																												if matrix[i][row] != 0:
																																			__UpperCAmelCase     ,						__UpperCAmelCase    :      str       = matrix[i], matrix[row]
																																			__UpperCAmelCase    :      List[Any]       = False
																																			break
																					if reduce:
																												rank -= 1
																												for i in range(_lowerCamelCase				):
																																			__UpperCAmelCase    :      Any       = matrix[i][rank]

																																			  # Reduce the row pointer by one to stay on the same row
																					row -= 1

							return rank


if __name__ == "__main__":
	import doctest

	doctest.testmod()












"""simple docstring"""





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


_SCREAMING_SNAKE_CASE   :							List[str]          =		{}

try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _SCREAMING_SNAKE_CASE   :							str          =		['''NllbTokenizer''']

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _SCREAMING_SNAKE_CASE   :							Optional[Any]          =		['''NllbTokenizerFast''']


if TYPE_CHECKING:
  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_nllb import NllbTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_nllb_fast import NllbTokenizerFast

else:
  import sys

  _SCREAMING_SNAKE_CASE   :							Any          =		_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




